BEAM

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

BEAM: Set Beam Parameters

Many commands in MAD-X require the setting of various quantities related to the beam in the machine. Therefore, MAD-X will stop with a fatal error if an attempt is made to expand (USE) a sequence for which no BEAM command has been issued before.

The quantities are entered by a BEAM command:

BEAM, PARTICLE=name,MASS=real,CHARGE=real,
      ENERGY=real,PC=real,GAMMA=real,
      EX=real,EXN=real,EY=real,EYN=real,
      ET=real,SIGT=real,SIGE=real,
      KBUNCH=integer,NPART=real,BCURRENT=real,
      BUNCHED=logical,RADIATE=logical,BV=integer,SEQUENCE=name;

Warning: BEAM updates, i. e. it replaces attributes explicitely mentioned, but does not return to default values for others! To reset to beam value defaults, use RESBEAM. The particle restmass and charge are defined by:

PARTICLE: The name of particles in the machine. MAD knows the restmass and the charge for the following particles:
- POSITRON: The particles are positrons (MASS=m_e, CHARGE=1),
- ELECTRON: The particles are electrons (MASS=m_e, CHARGE=-1),
- PROTON: The particles are protons (MASS=m_p, CHARGE=1),
- ANTIPROTON: The particles are anti-protons (MASS=m_p, CHARGE=-1).
- POSMUON: The particles are positive muons (MASS=m_mu, CHARGE=1),
- NEGMUON: The particles are negative muons (MASS=m_mu, CHARGE=-1).

Therefore neither restmass nor charge can be modified for these predefined particles. On the other hand, for ions and all other user defined particles the name, restmass, and charge can be entered independently.

By default the total particle energy is 1 GeV. A different value can be defined by one of the following:

ENERGY: The total energy per particle in GeV. If given, it must be greater then the particle restmass.
PC: The momentum per particle in GeV/c. If given, it must be greater than zero.
GAMMA: The ratio between total energy and rest energy of the particles: GAMMA = E / m₀. If given, it must be greater than one. If the restmass is changed a new value for the energy should be entered. Otherwise the energy remains unchanged, and the momentum PC and the quantity GAMMA are recalculated. The emittances are defined by:
EX: The horizontal emittance E_x (default: 1 m).
EY: The vertical emittance E_y (default: 1 m).
ET: The longitudinal emittance E_t (default: 1 m). The emittances can be replaced by the normalised emittances and the energy spread:
EXN: The normalised horizontal emittance [m]: E_xn = 4 (GAMMA² - 1)^1/2 E_x (ignored if E_x is given).
EYN: The normalised vertical emittance [m]: E_yn = 4 (GAMMA² - 1)^1/2 E_y (ignored if E_x is given).
SIGT: The bunch length c sigma(t) in [m].
SIGE: The relative energy spread sigma(E)/E in [1].

Certain commands compute the synchrotron tune Q_s from the RF cavities. If Q_s is non-zero, the relative energy spread and the bunch length are

sigma(E) / p₀ c = (2 pi Q_s E_t / ETA C)^1/2,

c sigma(t) = (ETA C E_t / 2 pi Q_s)^1/2.

C is the machine circumference, and

ETA = GAMMA^-2 - GAMMA(transition)^-2.

The order of precedence in the parameter evaluation is given below:

    particle->(mass+charge)
    energy->pc->gamma->beta
    ex->exn
    ey->eyn
    current->npart
    et->sigt->sige

where any item to the left takes precendence over the others.

Finally, the BEAM command accepts

KBUNCH: The number of particle bunches in the machine (default: 1).
NPART: The number of particles per bunch (default: 0).
BCURRENT: The bunch current (default: 0 A).
BUNCHED: A logical flag. If set, the beam is treated as bunched whenever this makes sense.
RADIATE: A logical flag. If set, synchrotron radiation is considered in all bipolar magnets.
BV: an integer specifying the direction of the particle movement in a beam line; either +1 (default), or -1. For a detailed explanation see under bv flag.
SEQUENCE: this attaches the beam command to a specific sequence; if the name is omitted, the BEAM command refers to the default beam always present. Sequences without attached beam use this default beam. When updating a beam, the corresponding sequence name, if any, must always be mentioned.

The BEAM command changes only the parameters entered. The command RESBEAM resets all beam data to their beam value defaults.

Examples:

BEAM,   PARTICLE=ELECTRON,ENERGY=50,EX=1.E-6,EY=1.E-8,SIGE=1.E-3;
 ...
BEAM,   RADIATE;
 ...
RESBEAM;
BEAM,   EX=2.E-5,EY=3.E-7,SIGE=4.E-3;

The first command selects electrons, and sets energy and emittances. The second one turns on synchrotron radiation. The last two select positrons (by default), set the energy to 1 GeV (default), clear the synchrotron radiation flag, and set the emittances to the values entered.

Some program modules of MAD-X may also store data into a beam data block. Expressions may refer to data in this beam data block using the notation

BEAM->attribute-name

BEAM%sequence->attribute-name.

This notation refers to the value of attribute-name found in the default BEAM resp. the beam belonging to the sequence given. This can be used for receiving or using values, e.g.

value,beam%lhcb2->bv;

or for storing values in the beam (this does NOT trigger an update of dependent variables !), e.g.

beam->charge=-1;

The current values in the BEAM bank can be obtained by the command

show,beam;

resp.

show,beam%sequence;

hansg 11.9.2000